LMFDB - Embedded newform 2240.2.bd.a.561.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2240,2,Mod(561,2240)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2240.561");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2240 = 2^{6} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2240.bd (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.8864900528$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 560)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			561.13
Character	$\chi$	$=$	2240.561
Dual form			2240.2.bd.a.1681.13

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.576404 - 0.576404i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} +2.33552i q^{9} +O(q^{10})$	\(q+(0.576404 - 0.576404i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} +2.33552i q^{9} +(-2.93187 - 2.93187i) q^{11} +(-1.89090 + 1.89090i) q^{13} +0.815159 q^{15} +1.43655 q^{17} +(-1.45281 + 1.45281i) q^{19} +(-0.576404 - 0.576404i) q^{21} +8.06848i q^{23} +1.00000i q^{25} +(3.07541 + 3.07541i) q^{27} +(2.86338 - 2.86338i) q^{29} +1.31281 q^{31} -3.37988 q^{33} +(0.707107 - 0.707107i) q^{35} +(6.64315 + 6.64315i) q^{37} +2.17984i q^{39} +8.42537i q^{41} +(1.52206 + 1.52206i) q^{43} +(-1.65146 + 1.65146i) q^{45} +7.14252 q^{47} -1.00000 q^{49} +(0.828034 - 0.828034i) q^{51} +(-4.13783 - 4.13783i) q^{53} -4.14628i q^{55} +1.67481i q^{57} +(5.34634 + 5.34634i) q^{59} +(-3.30135 + 3.30135i) q^{61} +2.33552 q^{63} -2.67413 q^{65} +(-5.94425 + 5.94425i) q^{67} +(4.65071 + 4.65071i) q^{69} +4.72606i q^{71} -14.9033i q^{73} +(0.576404 + 0.576404i) q^{75} +(-2.93187 + 2.93187i) q^{77} +10.3784 q^{79} -3.46118 q^{81} +(0.898977 - 0.898977i) q^{83} +(1.01580 + 1.01580i) q^{85} -3.30093i q^{87} +11.5205i q^{89} +(1.89090 + 1.89090i) q^{91} +(0.756707 - 0.756707i) q^{93} -2.05459 q^{95} -13.1190 q^{97} +(6.84742 - 6.84742i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q+O(q^{10}) $ 44 * q	$ 44 q - 12 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 12 q^{29} + 28 q^{37} + 44 q^{43} - 44 q^{49} + 8 q^{51} - 12 q^{53} - 24 q^{59} - 16 q^{61} - 28 q^{63} - 40 q^{65} + 28 q^{67} + 40 q^{69} - 12 q^{77} + 16 q^{79} + 20 q^{81} + 16 q^{85} + 88 q^{93} + 32 q^{95} - 28 q^{99}+O(q^{100}) $ 44 * q - 12 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 12 * q^29 + 28 * q^37 + 44 * q^43 - 44 * q^49 + 8 * q^51 - 12 * q^53 - 24 * q^59 - 16 * q^61 - 28 * q^63 - 40 * q^65 + 28 * q^67 + 40 * q^69 - 12 * q^77 + 16 * q^79 + 20 * q^81 + 16 * q^85 + 88 * q^93 + 32 * q^95 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times$.

$n$	$897$	$1471$	$1541$	$1921$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.576404	−	0.576404i	0.332787	−	0.332787i	−0.520857	−	0.853644i	$-0.674387\pi$
$3$	0.576404	−	0.576404i	0.332787	−	0.332787i	0.853644	+	0.520857i	$0.174387\pi$
$4$		0			0
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		0			0
$9$			2.33552i			0.778505i
$10$		0			0
$11$	−2.93187	−	2.93187i	−0.883991	−	0.883991i	0.109947	−	0.993937i	$-0.464932\pi$
$11$	−2.93187	−	2.93187i	−0.883991	−	0.883991i	−0.993937	+	0.109947i	$0.964932\pi$
$12$		0			0
$13$	−1.89090	+	1.89090i	−0.524441	+	0.524441i	−0.918909	−	0.394469i	$-0.870929\pi$
$13$	−1.89090	+	1.89090i	−0.524441	+	0.524441i	0.394469	+	0.918909i	$0.370929\pi$
$14$		0			0
$15$	0.815159			0.210473
$16$		0			0
$17$	1.43655			0.348415			0.174207	−	0.984709i	$-0.444264\pi$
$17$	1.43655			0.348415			0.174207	+	0.984709i	$0.444264\pi$
$18$		0			0
$19$	−1.45281	+	1.45281i	−0.333298	+	0.333298i	−0.853837	−	0.520540i	$-0.825731\pi$
$19$	−1.45281	+	1.45281i	−0.333298	+	0.333298i	0.520540	+	0.853837i	$0.325731\pi$
$20$		0			0
$21$	−0.576404	−	0.576404i	−0.125782	−	0.125782i
$22$		0			0
$23$			8.06848i			1.68239i	0.540729	+	0.841197i	$0.318149\pi$
$23$			8.06848i			1.68239i	−0.540729	+	0.841197i	$0.681851\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	3.07541	+	3.07541i	0.591864	+	0.591864i
$28$		0			0
$29$	2.86338	−	2.86338i	0.531717	−	0.531717i	−0.389366	−	0.921083i	$-0.627306\pi$
$29$	2.86338	−	2.86338i	0.531717	−	0.531717i	0.921083	+	0.389366i	$0.127306\pi$
$30$		0			0
$31$	1.31281			0.235787			0.117893	−	0.993026i	$-0.462386\pi$
$31$	1.31281			0.235787			0.117893	+	0.993026i	$0.462386\pi$
$32$		0			0
$33$	−3.37988			−0.588361
$34$		0			0
$35$	0.707107	−	0.707107i	0.119523	−	0.119523i
$36$		0			0
$37$	6.64315	+	6.64315i	1.09213	+	1.09213i	0.995301	+	0.0968262i	$0.0308691\pi$
$37$	6.64315	+	6.64315i	1.09213	+	1.09213i	0.0968262	+	0.995301i	$0.469131\pi$
$38$		0			0
$39$			2.17984i			0.349054i
$40$		0			0
$41$			8.42537i			1.31582i	0.753096	+	0.657911i	$0.228560\pi$
$41$			8.42537i			1.31582i	−0.753096	+	0.657911i	$0.771440\pi$
$42$		0			0
$43$	1.52206	+	1.52206i	0.232112	+	0.232112i	0.813574	−	0.581462i	$-0.197519\pi$
$43$	1.52206	+	1.52206i	0.232112	+	0.232112i	−0.581462	+	0.813574i	$0.697519\pi$
$44$		0			0
$45$	−1.65146	+	1.65146i	−0.246185	+	0.246185i
$46$		0			0
$47$	7.14252			1.04184			0.520922	−	0.853604i	$-0.325588\pi$
$47$	7.14252			1.04184			0.520922	+	0.853604i	$0.325588\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	0.828034	−	0.828034i	0.115948	−	0.115948i
$52$		0			0
$53$	−4.13783	−	4.13783i	−0.568375	−	0.568375i	0.363298	−	0.931673i	$-0.381651\pi$
$53$	−4.13783	−	4.13783i	−0.568375	−	0.568375i	−0.931673	+	0.363298i	$0.881651\pi$
$54$		0			0
$55$		−	4.14628i		−	0.559085i
$56$		0			0
$57$			1.67481i			0.221834i
$58$		0			0
$59$	5.34634	+	5.34634i	0.696034	+	0.696034i	0.963553	−	0.267518i	$-0.0862036\pi$
$59$	5.34634	+	5.34634i	0.696034	+	0.696034i	−0.267518	+	0.963553i	$0.586204\pi$
$60$		0			0
$61$	−3.30135	+	3.30135i	−0.422695	+	0.422695i	−0.886131	−	0.463436i	$-0.846617\pi$
$61$	−3.30135	+	3.30135i	−0.422695	+	0.422695i	0.463436	+	0.886131i	$0.346617\pi$
$62$		0			0
$63$	2.33552			0.294247
$64$		0			0
$65$	−2.67413			−0.331686
$66$		0			0
$67$	−5.94425	+	5.94425i	−0.726206	+	0.726206i	−0.969862	−	0.243656i	$-0.921653\pi$
$67$	−5.94425	+	5.94425i	−0.726206	+	0.726206i	0.243656	+	0.969862i	$0.421653\pi$
$68$		0			0
$69$	4.65071	+	4.65071i	0.559879	+	0.559879i
$70$		0			0
$71$			4.72606i			0.560881i	0.959871	+	0.280440i	$0.0904805\pi$
$71$			4.72606i			0.560881i	−0.959871	+	0.280440i	$0.909520\pi$
$72$		0			0
$73$		−	14.9033i		−	1.74430i	−0.489237	−	0.872151i	$-0.662725\pi$
$73$		−	14.9033i		−	1.74430i	0.489237	−	0.872151i	$-0.337275\pi$
$74$		0			0
$75$	0.576404	+	0.576404i	0.0665574	+	0.0665574i
$76$		0			0
$77$	−2.93187	+	2.93187i	−0.334117	+	0.334117i
$78$		0			0
$79$	10.3784			1.16766			0.583832	−	0.811875i	$-0.301553\pi$
$79$	10.3784			1.16766			0.583832	+	0.811875i	$0.301553\pi$
$80$		0			0
$81$	−3.46118			−0.384576
$82$		0			0
$83$	0.898977	−	0.898977i	0.0986755	−	0.0986755i	−0.656046	−	0.754721i	$-0.727772\pi$
$83$	0.898977	−	0.898977i	0.0986755	−	0.0986755i	0.754721	+	0.656046i	$0.227772\pi$
$84$		0			0
$85$	1.01580	+	1.01580i	0.110178	+	0.110178i
$86$		0			0
$87$		−	3.30093i		−	0.353897i
$88$		0			0
$89$			11.5205i			1.22117i	0.791951	+	0.610585i	$0.209066\pi$
$89$			11.5205i			1.22117i	−0.791951	+	0.610585i	$0.790934\pi$
$90$		0			0
$91$	1.89090	+	1.89090i	0.198220	+	0.198220i
$92$		0			0
$93$	0.756707	−	0.756707i	0.0784669	−	0.0784669i
$94$		0			0
$95$	−2.05459			−0.210796
$96$		0			0
$97$	−13.1190			−1.33203			−0.666016	−	0.745937i	$-0.732002\pi$
$97$	−13.1190			−1.33203			−0.666016	+	0.745937i	$0.732002\pi$
$98$		0			0
$99$	6.84742	−	6.84742i	0.688191	−	0.688191i
$100$		0			0
$101$	0.844747	+	0.844747i	0.0840554	+	0.0840554i	0.747884	−	0.663829i	$-0.231070\pi$
$101$	0.844747	+	0.844747i	0.0840554	+	0.0840554i	−0.663829	+	0.747884i	$0.731070\pi$
$102$		0			0
$103$			15.3945i			1.51687i	0.651751	+	0.758433i	$0.274035\pi$
$103$			15.3945i			1.51687i	−0.651751	+	0.758433i	$0.725965\pi$
$104$		0			0
$105$		−	0.815159i		−	0.0795514i
$106$		0			0
$107$	−9.46571	−	9.46571i	−0.915085	−	0.915085i	0.0815817	−	0.996667i	$-0.474003\pi$
$107$	−9.46571	−	9.46571i	−0.915085	−	0.915085i	−0.996667	+	0.0815817i	$0.974003\pi$
$108$		0			0
$109$	7.59547	−	7.59547i	0.727514	−	0.727514i	−0.242610	−	0.970124i	$-0.578004\pi$
$109$	7.59547	−	7.59547i	0.727514	−	0.727514i	0.970124	+	0.242610i	$0.0780035\pi$
$110$		0			0
$111$	7.65828			0.726892
$112$		0			0
$113$	−8.31678			−0.782377			−0.391188	−	0.920311i	$-0.627936\pi$
$113$	−8.31678			−0.782377			−0.391188	+	0.920311i	$0.627936\pi$
$114$		0			0
$115$	−5.70528	+	5.70528i	−0.532020	+	0.532020i
$116$		0			0
$117$	−4.41622	−	4.41622i	−0.408280	−	0.408280i
$118$		0			0
$119$		−	1.43655i		−	0.131688i
$120$		0			0
$121$			6.19167i			0.562879i
$122$		0			0
$123$	4.85642	+	4.85642i	0.437889	+	0.437889i
$124$		0			0
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	9.91643			0.879941			0.439971	−	0.898012i	$-0.354989\pi$
$127$	9.91643			0.879941			0.439971	+	0.898012i	$0.354989\pi$
$128$		0			0
$129$	1.75464			0.154488
$130$		0			0
$131$	−3.31544	+	3.31544i	−0.289671	+	0.289671i	−0.836950	−	0.547279i	$-0.815664\pi$
$131$	−3.31544	+	3.31544i	−0.289671	+	0.289671i	0.547279	+	0.836950i	$0.315664\pi$
$132$		0			0
$133$	1.45281	+	1.45281i	0.125975	+	0.125975i
$134$		0			0
$135$			4.34929i			0.374328i
$136$		0			0
$137$			4.71440i			0.402778i	0.979511	+	0.201389i	$0.0645456\pi$
$137$			4.71440i			0.402778i	−0.979511	+	0.201389i	$0.935454\pi$
$138$		0			0
$139$	−13.9064	−	13.9064i	−1.17952	−	1.17952i	−0.979866	−	0.199657i	$-0.936017\pi$
$139$	−13.9064	−	13.9064i	−1.17952	−	1.17952i	−0.199657	−	0.979866i	$-0.563983\pi$
$140$		0			0
$141$	4.11698	−	4.11698i	0.346712	−	0.346712i
$142$		0			0
$143$	11.0877			0.927202
$144$		0			0
$145$	4.04944			0.336287
$146$		0			0
$147$	−0.576404	+	0.576404i	−0.0475410	+	0.0475410i
$148$		0			0
$149$	1.93605	+	1.93605i	0.158607	+	0.158607i	0.781949	−	0.623342i	$-0.214226\pi$
$149$	1.93605	+	1.93605i	0.158607	+	0.158607i	−0.623342	+	0.781949i	$0.714226\pi$
$150$		0			0
$151$			19.9549i			1.62391i	0.583722	+	0.811953i	$0.301596\pi$
$151$			19.9549i			1.62391i	−0.583722	+	0.811953i	$0.698404\pi$
$152$		0			0
$153$			3.35509i			0.271243i
$154$		0			0
$155$	0.928294	+	0.928294i	0.0745624	+	0.0745624i
$156$		0			0
$157$	12.8265	−	12.8265i	1.02367	−	1.02367i	0.0239570	−	0.999713i	$-0.492374\pi$
$157$	12.8265	−	12.8265i	1.02367	−	1.02367i	0.999713	−	0.0239570i	$-0.00762649\pi$
$158$		0			0
$159$	−4.77013			−0.378296
$160$		0			0
$161$	8.06848			0.635885
$162$		0			0
$163$	13.0681	−	13.0681i	1.02357	−	1.02357i	0.0238561	−	0.999715i	$-0.492406\pi$
$163$	13.0681	−	13.0681i	1.02357	−	1.02357i	0.999715	−	0.0238561i	$-0.00759437\pi$
$164$		0			0
$165$	−2.38994	−	2.38994i	−0.186056	−	0.186056i
$166$		0			0
$167$		−	6.72568i		−	0.520449i	−0.965548	−	0.260225i	$-0.916203\pi$
$167$		−	6.72568i		−	0.520449i	0.965548	−	0.260225i	$-0.0837966\pi$
$168$		0			0
$169$			5.84900i			0.449923i
$170$		0			0
$171$	−3.39306	−	3.39306i	−0.259474	−	0.259474i
$172$		0			0
$173$	1.72006	−	1.72006i	0.130774	−	0.130774i	−0.638690	−	0.769464i	$-0.720523\pi$
$173$	1.72006	−	1.72006i	0.130774	−	0.130774i	0.769464	+	0.638690i	$0.220523\pi$
$174$		0			0
$175$	1.00000			0.0755929
$176$		0			0
$177$	6.16331			0.463263
$178$		0			0
$179$	5.77336	−	5.77336i	0.431521	−	0.431521i	−0.457624	−	0.889146i	$-0.651300\pi$
$179$	5.77336	−	5.77336i	0.431521	−	0.431521i	0.889146	+	0.457624i	$0.151300\pi$
$180$		0			0
$181$	16.3185	+	16.3185i	1.21294	+	1.21294i	0.970054	+	0.242890i	$0.0780953\pi$
$181$	16.3185	+	16.3185i	1.21294	+	1.21294i	0.242890	+	0.970054i	$0.421905\pi$
$182$		0			0
$183$			3.80583i			0.281335i
$184$		0			0
$185$			9.39484i			0.690722i
$186$		0			0
$187$	−4.21177	−	4.21177i	−0.307995	−	0.307995i
$188$		0			0
$189$	3.07541	−	3.07541i	0.223703	−	0.223703i
$190$		0			0
$191$	−9.11341			−0.659423			−0.329712	−	0.944082i	$-0.606951\pi$
$191$	−9.11341			−0.659423			−0.329712	+	0.944082i	$0.606951\pi$
$192$		0			0
$193$	−4.16518			−0.299816			−0.149908	−	0.988700i	$-0.547898\pi$
$193$	−4.16518			−0.299816			−0.149908	+	0.988700i	$0.547898\pi$
$194$		0			0
$195$	−1.54138	+	1.54138i	−0.110381	+	0.110381i
$196$		0			0
$197$	−1.10761	−	1.10761i	−0.0789137	−	0.0789137i	0.666548	−	0.745462i	$-0.267771\pi$
$197$	−1.10761	−	1.10761i	−0.0789137	−	0.0789137i	−0.745462	+	0.666548i	$0.767771\pi$
$198$		0			0
$199$			6.87016i			0.487012i	0.969899	+	0.243506i	$0.0782976\pi$
$199$			6.87016i			0.487012i	−0.969899	+	0.243506i	$0.921702\pi$
$200$		0			0
$201$			6.85259i			0.483344i
$202$		0			0
$203$	−2.86338	−	2.86338i	−0.200970	−	0.200970i
$204$		0			0
$205$	−5.95764	+	5.95764i	−0.416099	+	0.416099i
$206$		0			0
$207$	−18.8441			−1.30975
$208$		0			0
$209$	8.51889			0.589264
$210$		0			0
$211$	−12.8720	+	12.8720i	−0.886147	+	0.886147i	−0.994151	−	0.108004i	$-0.965554\pi$
$211$	−12.8720	+	12.8720i	−0.886147	+	0.886147i	0.108004	+	0.994151i	$0.465554\pi$
$212$		0			0
$213$	2.72412	+	2.72412i	0.186654	+	0.186654i
$214$		0			0
$215$			2.15252i			0.146801i
$216$		0			0
$217$		−	1.31281i		−	0.0891191i
$218$		0			0
$219$	−8.59034	−	8.59034i	−0.580481	−	0.580481i
$220$		0			0
$221$	−2.71637	+	2.71637i	−0.182723	+	0.182723i
$222$		0			0
$223$	19.4690			1.30374			0.651869	−	0.758331i	$-0.273985\pi$
$223$	19.4690			1.30374			0.651869	+	0.758331i	$0.273985\pi$
$224$		0			0
$225$	−2.33552			−0.155701
$226$		0			0
$227$	−11.3381	+	11.3381i	−0.752534	+	0.752534i	−0.974952	−	0.222417i	$-0.928605\pi$
$227$	−11.3381	+	11.3381i	−0.752534	+	0.752534i	0.222417	+	0.974952i	$0.428605\pi$
$228$		0			0
$229$	−7.89978	−	7.89978i	−0.522032	−	0.522032i	0.396153	−	0.918185i	$-0.370345\pi$
$229$	−7.89978	−	7.89978i	−0.522032	−	0.522032i	−0.918185	+	0.396153i	$0.870345\pi$
$230$		0			0
$231$			3.37988i			0.222380i
$232$		0			0
$233$			13.8329i			0.906220i	0.891454	+	0.453110i	$0.149686\pi$
$233$			13.8329i			0.906220i	−0.891454	+	0.453110i	$0.850314\pi$
$234$		0			0
$235$	5.05052	+	5.05052i	0.329460	+	0.329460i
$236$		0			0
$237$	5.98217	−	5.98217i	0.388583	−	0.388583i
$238$		0			0
$239$	−5.85778			−0.378908			−0.189454	−	0.981890i	$-0.560672\pi$
$239$	−5.85778			−0.378908			−0.189454	+	0.981890i	$0.560672\pi$
$240$		0			0
$241$	1.98422			0.127815			0.0639075	−	0.997956i	$-0.479644\pi$
$241$	1.98422			0.127815			0.0639075	+	0.997956i	$0.479644\pi$
$242$		0			0
$243$	−11.2213	+	11.2213i	−0.719846	+	0.719846i
$244$		0			0
$245$	−0.707107	−	0.707107i	−0.0451754	−	0.0451754i
$246$		0			0
$247$		−	5.49424i		−	0.349590i
$248$		0			0
$249$		−	1.03635i		−	0.0656759i
$250$		0			0
$251$	−15.4038	−	15.4038i	−0.972279	−	0.972279i	0.0273470	−	0.999626i	$-0.491294\pi$
$251$	−15.4038	−	15.4038i	−0.972279	−	0.972279i	−0.999626	+	0.0273470i	$0.991294\pi$
$252$		0			0
$253$	23.6557	−	23.6557i	1.48722	−	1.48722i
$254$		0			0
$255$	1.17102			0.0733320
$256$		0			0
$257$	23.0075			1.43517			0.717583	−	0.696473i	$-0.245248\pi$
$257$	23.0075			1.43517			0.717583	+	0.696473i	$0.245248\pi$
$258$		0			0
$259$	6.64315	−	6.64315i	0.412785	−	0.412785i
$260$		0			0
$261$	6.68748	+	6.68748i	0.413945	+	0.413945i
$262$		0			0
$263$		−	7.62646i		−	0.470268i	−0.971963	−	0.235134i	$-0.924447\pi$
$263$		−	7.62646i		−	0.470268i	0.971963	−	0.235134i	$-0.0755529\pi$
$264$		0			0
$265$		−	5.85177i		−	0.359472i
$266$		0			0
$267$	6.64046	+	6.64046i	0.406390	+	0.406390i
$268$		0			0
$269$	13.0188	−	13.0188i	0.793768	−	0.793768i	−0.188336	−	0.982105i	$-0.560310\pi$
$269$	13.0188	−	13.0188i	0.793768	−	0.793768i	0.982105	+	0.188336i	$0.0603095\pi$
$270$		0			0
$271$	12.2396			0.743502			0.371751	−	0.928333i	$-0.378758\pi$
$271$	12.2396			0.743502			0.371751	+	0.928333i	$0.378758\pi$
$272$		0			0
$273$	2.17984			0.131930
$274$		0			0
$275$	2.93187	−	2.93187i	0.176798	−	0.176798i
$276$		0			0
$277$	−17.3921	−	17.3921i	−1.04499	−	1.04499i	−0.998939	−	0.0460511i	$-0.985336\pi$
$277$	−17.3921	−	17.3921i	−1.04499	−	1.04499i	−0.0460511	−	0.998939i	$-0.514664\pi$
$278$		0			0
$279$			3.06608i			0.183561i
$280$		0			0
$281$			23.7456i			1.41655i	0.705938	+	0.708273i	$0.250526\pi$
$281$			23.7456i			1.41655i	−0.705938	+	0.708273i	$0.749474\pi$
$282$		0			0
$283$	1.87152	+	1.87152i	0.111250	+	0.111250i	0.760541	−	0.649290i	$-0.224934\pi$
$283$	1.87152	+	1.87152i	0.111250	+	0.111250i	−0.649290	+	0.760541i	$0.724934\pi$
$284$		0			0
$285$	−1.18427	+	1.18427i	−0.0701502	+	0.0701502i
$286$		0			0
$287$	8.42537			0.497334
$288$		0			0
$289$	−14.9363			−0.878607
$290$		0			0
$291$	−7.56185	+	7.56185i	−0.443283	+	0.443283i
$292$		0			0
$293$	−18.5601	−	18.5601i	−1.08429	−	1.08429i	−0.996104	−	0.0881889i	$-0.971892\pi$
$293$	−18.5601	−	18.5601i	−1.08429	−	1.08429i	−0.0881889	−	0.996104i	$-0.528108\pi$
$294$		0			0
$295$			7.56087i			0.440211i
$296$		0			0
$297$		−	18.0334i		−	1.04640i
$298$		0			0
$299$	−15.2567	−	15.2567i	−0.882316	−	0.882316i
$300$		0			0
$301$	1.52206	−	1.52206i	0.0877301	−	0.0877301i
$302$		0			0
$303$	0.973831			0.0559451
$304$		0			0
$305$	−4.66882			−0.267336
$306$		0			0
$307$	16.3790	−	16.3790i	0.934799	−	0.934799i	−0.0632014	−	0.998001i	$-0.520131\pi$
$307$	16.3790	−	16.3790i	0.934799	−	0.934799i	0.998001	+	0.0632014i	$0.0201311\pi$
$308$		0			0
$309$	8.87346	+	8.87346i	0.504793	+	0.504793i
$310$		0			0
$311$			6.38044i			0.361802i	0.983501	+	0.180901i	$0.0579013\pi$
$311$			6.38044i			0.361802i	−0.983501	+	0.180901i	$0.942099\pi$
$312$		0			0
$313$		−	15.8278i		−	0.894637i	−0.894375	−	0.447319i	$-0.852379\pi$
$313$		−	15.8278i		−	0.894637i	0.894375	−	0.447319i	$-0.147621\pi$
$314$		0			0
$315$	1.65146	+	1.65146i	0.0930492	+	0.0930492i
$316$		0			0
$317$	−10.6420	+	10.6420i	−0.597713	+	0.597713i	−0.939703	−	0.341991i	$-0.888899\pi$
$317$	−10.6420	+	10.6420i	−0.597713	+	0.597713i	0.341991	+	0.939703i	$0.388899\pi$
$318$		0			0
$319$	−16.7901			−0.940066
$320$		0			0
$321$	−10.9122			−0.609057
$322$		0			0
$323$	−2.08704	+	2.08704i	−0.116126	+	0.116126i
$324$		0			0
$325$	−1.89090	−	1.89090i	−0.104888	−	0.104888i
$326$		0			0
$327$		−	8.75612i		−	0.484215i
$328$		0			0
$329$		−	7.14252i		−	0.393780i
$330$		0			0
$331$	−5.56618	−	5.56618i	−0.305945	−	0.305945i	0.537389	−	0.843334i	$-0.319411\pi$
$331$	−5.56618	−	5.56618i	−0.305945	−	0.305945i	−0.843334	+	0.537389i	$0.819411\pi$
$332$		0			0
$333$	−15.5152	+	15.5152i	−0.850227	+	0.850227i
$334$		0			0
$335$	−8.40644			−0.459293
$336$		0			0
$337$	26.1199			1.42284			0.711420	−	0.702768i	$-0.248053\pi$
$337$	26.1199			1.42284			0.711420	+	0.702768i	$0.248053\pi$
$338$		0			0
$339$	−4.79383	+	4.79383i	−0.260365	+	0.260365i
$340$		0			0
$341$	−3.84897	−	3.84897i	−0.208433	−	0.208433i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$			6.57709i			0.354099i
$346$		0			0
$347$	−4.74109	−	4.74109i	−0.254515	−	0.254515i	0.568304	−	0.822819i	$-0.307600\pi$
$347$	−4.74109	−	4.74109i	−0.254515	−	0.254515i	−0.822819	+	0.568304i	$0.807600\pi$
$348$		0			0
$349$	18.3963	−	18.3963i	0.984730	−	0.984730i	−0.0151554	−	0.999885i	$-0.504824\pi$
$349$	18.3963	−	18.3963i	0.984730	−	0.984730i	0.999885	+	0.0151554i	$0.00482430\pi$
$350$		0			0
$351$	−11.6306			−0.620795
$352$		0			0
$353$	−29.0370			−1.54548			−0.772740	−	0.634722i	$-0.781115\pi$
$353$	−29.0370			−1.54548			−0.772740	+	0.634722i	$0.781115\pi$
$354$		0			0
$355$	−3.34183	+	3.34183i	−0.177366	+	0.177366i
$356$		0			0
$357$	−0.828034	−	0.828034i	−0.0438242	−	0.0438242i
$358$		0			0
$359$		−	35.0672i		−	1.85078i	−0.379019	−	0.925389i	$-0.623738\pi$
$359$		−	35.0672i		−	1.85078i	0.379019	−	0.925389i	$-0.376262\pi$
$360$		0			0
$361$			14.7787i			0.777825i
$362$		0			0
$363$	3.56890	+	3.56890i	0.187319	+	0.187319i
$364$		0			0
$365$	10.5382	−	10.5382i	0.551597	−	0.551597i
$366$		0			0
$367$	−17.5405			−0.915609			−0.457805	−	0.889053i	$-0.651364\pi$
$367$	−17.5405			−0.915609			−0.457805	+	0.889053i	$0.651364\pi$
$368$		0			0
$369$	−19.6776			−1.02437
$370$		0			0
$371$	−4.13783	+	4.13783i	−0.214825	+	0.214825i
$372$		0			0
$373$	10.3544	+	10.3544i	0.536129	+	0.536129i	0.922390	−	0.386260i	$-0.126233\pi$
$373$	10.3544	+	10.3544i	0.536129	+	0.536129i	−0.386260	+	0.922390i	$0.626233\pi$
$374$		0			0
$375$			0.815159i			0.0420946i
$376$		0			0
$377$			10.8287i			0.557708i
$378$		0			0
$379$	7.45748	+	7.45748i	0.383065	+	0.383065i	0.872205	−	0.489140i	$-0.162689\pi$
$379$	7.45748	+	7.45748i	0.383065	+	0.383065i	−0.489140	+	0.872205i	$0.662689\pi$
$380$		0			0
$381$	5.71587	−	5.71587i	0.292833	−	0.292833i
$382$		0			0
$383$	−1.24786			−0.0637628			−0.0318814	−	0.999492i	$-0.510150\pi$
$383$	−1.24786			−0.0637628			−0.0318814	+	0.999492i	$0.510150\pi$
$384$		0			0
$385$	−4.14628			−0.211314
$386$		0			0
$387$	−3.55480	+	3.55480i	−0.180700	+	0.180700i
$388$		0			0
$389$	16.6140	+	16.6140i	0.842364	+	0.842364i	0.989166	−	0.146802i	$-0.0468979\pi$
$389$	16.6140	+	16.6140i	0.842364	+	0.842364i	−0.146802	+	0.989166i	$0.546898\pi$
$390$		0			0
$391$			11.5908i			0.586171i
$392$		0			0
$393$			3.82207i			0.192798i
$394$		0			0
$395$	7.33865	+	7.33865i	0.369248	+	0.369248i
$396$		0			0
$397$	−0.525796	+	0.525796i	−0.0263889	+	0.0263889i	−0.720178	−	0.693789i	$-0.755940\pi$
$397$	−0.525796	+	0.525796i	−0.0263889	+	0.0263889i	0.693789	+	0.720178i	$0.255940\pi$
$398$		0			0
$399$	1.67481			0.0838455
$400$		0			0
$401$	12.9862			0.648499			0.324249	−	0.945972i	$-0.394888\pi$
$401$	12.9862			0.648499			0.324249	+	0.945972i	$0.394888\pi$
$402$		0			0
$403$	−2.48238	+	2.48238i	−0.123656	+	0.123656i
$404$		0			0
$405$	−2.44743	−	2.44743i	−0.121614	−	0.121614i
$406$		0			0
$407$		−	38.9537i		−	1.93086i
$408$		0			0
$409$			1.62193i			0.0801994i	0.999196	+	0.0400997i	$0.0127676\pi$
$409$			1.62193i			0.0801994i	−0.999196	+	0.0400997i	$0.987232\pi$
$410$		0			0
$411$	2.71740	+	2.71740i	0.134039	+	0.134039i
$412$		0			0
$413$	5.34634	−	5.34634i	0.263076	−	0.263076i
$414$		0			0
$415$	1.27135			0.0624079
$416$		0			0
$417$	−16.0314			−0.785060
$418$		0			0
$419$	15.0499	−	15.0499i	0.735234	−	0.735234i	−0.236418	−	0.971652i	$-0.575973\pi$
$419$	15.0499	−	15.0499i	0.735234	−	0.735234i	0.971652	+	0.236418i	$0.0759733\pi$
$420$		0			0
$421$	−4.91730	−	4.91730i	−0.239654	−	0.239654i	0.577053	−	0.816707i	$-0.304203\pi$
$421$	−4.91730	−	4.91730i	−0.239654	−	0.239654i	−0.816707	+	0.577053i	$0.804203\pi$
$422$		0			0
$423$			16.6815i			0.811081i
$424$		0			0
$425$			1.43655i			0.0696830i
$426$		0			0
$427$	3.30135	+	3.30135i	0.159764	+	0.159764i
$428$		0			0
$429$	6.39101	−	6.39101i	0.308561	−	0.308561i
$430$		0			0
$431$	−29.5936			−1.42547			−0.712737	−	0.701431i	$-0.752545\pi$
$431$	−29.5936			−1.42547			−0.712737	+	0.701431i	$0.752545\pi$
$432$		0			0
$433$	32.1447			1.54477			0.772387	−	0.635152i	$-0.219062\pi$
$433$	32.1447			1.54477			0.772387	+	0.635152i	$0.219062\pi$
$434$		0			0
$435$	2.33411	−	2.33411i	0.111912	−	0.111912i
$436$		0			0
$437$	−11.7220	−	11.7220i	−0.560738	−	0.560738i
$438$		0			0
$439$			25.8338i			1.23298i	0.787362	+	0.616491i	$0.211446\pi$
$439$			25.8338i			1.23298i	−0.787362	+	0.616491i	$0.788554\pi$
$440$		0			0
$441$		−	2.33552i		−	0.111215i
$442$		0			0
$443$	−15.9032	−	15.9032i	−0.755584	−	0.755584i	0.219932	−	0.975515i	$-0.429417\pi$
$443$	−15.9032	−	15.9032i	−0.755584	−	0.755584i	−0.975515	+	0.219932i	$0.929417\pi$
$444$		0			0
$445$	−8.14622	+	8.14622i	−0.386168	+	0.386168i
$446$		0			0
$447$	2.23189			0.105565
$448$		0			0
$449$	−39.7227			−1.87463			−0.937314	−	0.348486i	$-0.886696\pi$
$449$	−39.7227			−1.87463			−0.937314	+	0.348486i	$0.886696\pi$
$450$		0			0
$451$	24.7020	−	24.7020i	1.16317	−	1.16317i
$452$		0			0
$453$	11.5021	+	11.5021i	0.540415	+	0.540415i
$454$		0			0
$455$			2.67413i			0.125365i
$456$		0			0
$457$		−	19.4173i		−	0.908305i	−0.890924	−	0.454152i	$-0.849942\pi$
$457$		−	19.4173i		−	0.908305i	0.890924	−	0.454152i	$-0.150058\pi$
$458$		0			0
$459$	4.41799	+	4.41799i	0.206214	+	0.206214i
$460$		0			0
$461$	−17.8949	+	17.8949i	−0.833450	+	0.833450i	−0.987987	−	0.154537i	$-0.950611\pi$
$461$	−17.8949	+	17.8949i	−0.833450	+	0.833450i	0.154537	+	0.987987i	$0.450611\pi$
$462$		0			0
$463$	−5.40153			−0.251030			−0.125515	−	0.992092i	$-0.540058\pi$
$463$	−5.40153			−0.251030			−0.125515	+	0.992092i	$0.540058\pi$
$464$		0			0
$465$	1.07015			0.0496268
$466$		0			0
$467$	7.02850	−	7.02850i	0.325240	−	0.325240i	−0.525533	−	0.850773i	$-0.676134\pi$
$467$	7.02850	−	7.02850i	0.325240	−	0.325240i	0.850773	+	0.525533i	$0.176134\pi$
$468$		0			0
$469$	5.94425	+	5.94425i	0.274480	+	0.274480i
$470$		0			0
$471$		−	14.7866i		−	0.681329i
$472$		0			0
$473$		−	8.92495i		−	0.410370i
$474$		0			0
$475$	−1.45281	−	1.45281i	−0.0666595	−	0.0666595i
$476$		0			0
$477$	9.66397	−	9.66397i	0.442483	−	0.442483i
$478$		0			0
$479$	31.6205			1.44478			0.722388	−	0.691488i	$-0.243044\pi$
$479$	31.6205			1.44478			0.722388	+	0.691488i	$0.243044\pi$
$480$		0			0
$481$	−25.1231			−1.14551
$482$		0			0
$483$	4.65071	−	4.65071i	0.211614	−	0.211614i
$484$		0			0
$485$	−9.27653	−	9.27653i	−0.421226	−	0.421226i
$486$		0			0
$487$		−	6.89453i		−	0.312421i	−0.987724	−	0.156211i	$-0.950072\pi$
$487$		−	6.89453i		−	0.312421i	0.987724	−	0.156211i	$-0.0499279\pi$
$488$		0			0
$489$		−	15.0650i		−	0.681263i
$490$		0			0
$491$	14.0393	+	14.0393i	0.633584	+	0.633584i	0.948965	−	0.315381i	$-0.102132\pi$
$491$	14.0393	+	14.0393i	0.633584	+	0.633584i	−0.315381	+	0.948965i	$0.602132\pi$
$492$		0			0
$493$	4.11340	−	4.11340i	0.185258	−	0.185258i
$494$		0			0
$495$	9.68371			0.435250
$496$		0			0
$497$	4.72606			0.211993
$498$		0			0
$499$	−0.917846	+	0.917846i	−0.0410884	+	0.0410884i	−0.727352	−	0.686264i	$-0.759249\pi$
$499$	−0.917846	+	0.917846i	−0.0410884	+	0.0410884i	0.686264	+	0.727352i	$0.259249\pi$
$500$		0			0
$501$	−3.87671	−	3.87671i	−0.173199	−	0.173199i
$502$		0			0
$503$		−	9.74277i		−	0.434408i	−0.976126	−	0.217204i	$-0.930306\pi$
$503$		−	9.74277i		−	0.434408i	0.976126	−	0.217204i	$-0.0696938\pi$
$504$		0			0
$505$			1.19465i			0.0531613i
$506$		0			0
$507$	3.37139	+	3.37139i	0.149729	+	0.149729i
$508$		0			0
$509$	−6.51544	+	6.51544i	−0.288792	+	0.288792i	−0.836602	−	0.547811i	$-0.815461\pi$
$509$	−6.51544	+	6.51544i	−0.288792	+	0.288792i	0.547811	+	0.836602i	$0.315461\pi$
$510$		0			0
$511$	−14.9033			−0.659284
$512$		0			0
$513$	−8.93599			−0.394534
$514$		0			0
$515$	−10.8856	+	10.8856i	−0.479675	+	0.479675i
$516$		0			0
$517$	−20.9409	−	20.9409i	−0.920980	−	0.920980i
$518$		0			0
$519$		−	1.98290i		−	0.0870399i
$520$		0			0
$521$		−	10.2045i		−	0.447066i	−0.974696	−	0.223533i	$-0.928241\pi$
$521$		−	10.2045i		−	0.447066i	0.974696	−	0.223533i	$-0.0717590\pi$
$522$		0			0
$523$	−22.0914	−	22.0914i	−0.965988	−	0.965988i	0.0334527	−	0.999440i	$-0.489350\pi$
$523$	−22.0914	−	22.0914i	−0.965988	−	0.965988i	−0.999440	+	0.0334527i	$0.989350\pi$
$524$		0			0
$525$	0.576404	−	0.576404i	0.0251563	−	0.0251563i
$526$		0			0
$527$	1.88591			0.0821517
$528$		0			0
$529$	−42.1003			−1.83045
$530$		0			0
$531$	−12.4865	+	12.4865i	−0.541867	+	0.541867i
$532$		0			0
$533$	−15.9315	−	15.9315i	−0.690071	−	0.690071i
$534$		0			0
$535$		−	13.3865i		−	0.578751i
$536$		0			0
$537$		−	6.65558i		−	0.287209i
$538$		0			0
$539$	2.93187	+	2.93187i	0.126284	+	0.126284i
$540$		0			0
$541$	−20.4475	+	20.4475i	−0.879106	+	0.879106i	−0.993442	−	0.114336i	$-0.963526\pi$
$541$	−20.4475	+	20.4475i	−0.879106	+	0.879106i	0.114336	+	0.993442i	$0.463526\pi$
$542$		0			0
$543$	18.8121			0.807304
$544$		0			0
$545$	10.7416			0.460120
$546$		0			0
$547$	14.3509	−	14.3509i	0.613602	−	0.613602i	−0.330281	−	0.943883i	$-0.607144\pi$
$547$	14.3509	−	14.3509i	0.613602	−	0.613602i	0.943883	+	0.330281i	$0.107144\pi$
$548$		0			0
$549$	−7.71037	−	7.71037i	−0.329070	−	0.329070i
$550$		0			0
$551$			8.31991i			0.354440i
$552$		0			0
$553$		−	10.3784i		−	0.441335i
$554$		0			0
$555$	5.41522	+	5.41522i	0.229863	+	0.229863i
$556$		0			0
$557$	−18.6540	+	18.6540i	−0.790394	+	0.790394i	−0.981558	−	0.191164i	$-0.938774\pi$
$557$	−18.6540	+	18.6540i	−0.790394	+	0.790394i	0.191164	+	0.981558i	$0.438774\pi$
$558$		0			0
$559$	−5.75612			−0.243458
$560$		0			0
$561$	−4.85537			−0.204994
$562$		0			0
$563$	19.7090	−	19.7090i	0.830637	−	0.830637i	−0.156967	−	0.987604i	$-0.550171\pi$
$563$	19.7090	−	19.7090i	0.830637	−	0.830637i	0.987604	+	0.156967i	$0.0501715\pi$
$564$		0			0
$565$	−5.88085	−	5.88085i	−0.247409	−	0.247409i
$566$		0			0
$567$			3.46118i			0.145356i
$568$		0			0
$569$		−	16.5605i		−	0.694251i	−0.937819	−	0.347125i	$-0.887158\pi$
$569$		−	16.5605i		−	0.694251i	0.937819	−	0.347125i	$-0.112842\pi$
$570$		0			0
$571$	−4.59853	−	4.59853i	−0.192443	−	0.192443i	0.604308	−	0.796751i	$-0.293450\pi$
$571$	−4.59853	−	4.59853i	−0.192443	−	0.192443i	−0.796751	+	0.604308i	$0.793450\pi$
$572$		0			0
$573$	−5.25301	+	5.25301i	−0.219448	+	0.219448i
$574$		0			0
$575$	−8.06848			−0.336479
$576$		0			0
$577$	36.0984			1.50280			0.751399	−	0.659849i	$-0.229380\pi$
$577$	36.0984			1.50280			0.751399	+	0.659849i	$0.229380\pi$
$578$		0			0
$579$	−2.40083	+	2.40083i	−0.0997749	+	0.0997749i
$580$		0			0
$581$	−0.898977	−	0.898977i	−0.0372958	−	0.0372958i
$582$		0			0
$583$			24.2631i			1.00488i
$584$		0			0
$585$		−	6.24548i		−	0.258219i
$586$		0			0
$587$	−17.1069	−	17.1069i	−0.706077	−	0.706077i	0.259631	−	0.965708i	$-0.416399\pi$
$587$	−17.1069	−	17.1069i	−0.706077	−	0.706077i	−0.965708	+	0.259631i	$0.916399\pi$
$588$		0			0
$589$	−1.90726	+	1.90726i	−0.0785872	+	0.0785872i
$590$		0			0
$591$	−1.27686			−0.0525230
$592$		0			0
$593$	−14.3899			−0.590923			−0.295462	−	0.955355i	$-0.595473\pi$
$593$	−14.3899			−0.590923			−0.295462	+	0.955355i	$0.595473\pi$
$594$		0			0
$595$	1.01580	−	1.01580i	0.0416435	−	0.0416435i
$596$		0			0
$597$	3.95999	+	3.95999i	0.162072	+	0.162072i
$598$		0			0
$599$			19.5613i			0.799253i	0.916678	+	0.399627i	$0.130860\pi$
$599$			19.5613i			0.799253i	−0.916678	+	0.399627i	$0.869140\pi$
$600$		0			0
$601$		−	47.6643i		−	1.94427i	−0.234425	−	0.972134i	$-0.575321\pi$
$601$		−	47.6643i		−	1.94427i	0.234425	−	0.972134i	$-0.424679\pi$
$602$		0			0
$603$	−13.8829	−	13.8829i	−0.565355	−	0.565355i
$604$		0			0
$605$	−4.37817	+	4.37817i	−0.177998	+	0.177998i
$606$		0			0
$607$	32.9334			1.33673			0.668363	−	0.743835i	$-0.266995\pi$
$607$	32.9334			1.33673			0.668363	+	0.743835i	$0.266995\pi$
$608$		0			0
$609$	−3.30093			−0.133761
$610$		0			0
$611$	−13.5058	+	13.5058i	−0.546385	+	0.546385i
$612$		0			0
$613$	−14.2556	−	14.2556i	−0.575780	−	0.575780i	0.357958	−	0.933738i	$-0.383473\pi$
$613$	−14.2556	−	14.2556i	−0.575780	−	0.575780i	−0.933738	+	0.357958i	$0.883473\pi$
$614$		0			0
$615$			6.86801i			0.276945i
$616$		0			0
$617$		−	2.44103i		−	0.0982722i	−0.998792	−	0.0491361i	$-0.984353\pi$
$617$		−	2.44103i		−	0.0982722i	0.998792	−	0.0491361i	$-0.0156468\pi$
$618$		0			0
$619$	11.0216	+	11.0216i	0.442995	+	0.442995i	0.893017	−	0.450023i	$-0.148584\pi$
$619$	11.0216	+	11.0216i	0.442995	+	0.442995i	−0.450023	+	0.893017i	$0.648584\pi$
$620$		0			0
$621$	−24.8139	+	24.8139i	−0.995748	+	0.995748i
$622$		0			0
$623$	11.5205			0.461559
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	4.91033	−	4.91033i	0.196100	−	0.196100i
$628$		0			0
$629$	9.54323	+	9.54323i	0.380513	+	0.380513i
$630$		0			0
$631$		−	26.6244i		−	1.05990i	−0.848029	−	0.529950i	$-0.822211\pi$
$631$		−	26.6244i		−	1.05990i	0.848029	−	0.529950i	$-0.177789\pi$
$632$		0			0
$633$			14.8390i			0.589797i
$634$		0			0
$635$	7.01198	+	7.01198i	0.278262	+	0.278262i
$636$		0			0
$637$	1.89090	−	1.89090i	0.0749201	−	0.0749201i
$638$		0			0
$639$	−11.0378			−0.436649
$640$		0			0
$641$	−16.4913			−0.651367			−0.325684	−	0.945479i	$-0.605594\pi$
$641$	−16.4913			−0.651367			−0.325684	+	0.945479i	$0.605594\pi$
$642$		0			0
$643$	10.1394	−	10.1394i	0.399859	−	0.399859i	−0.478324	−	0.878183i	$-0.658756\pi$
$643$	10.1394	−	10.1394i	0.399859	−	0.399859i	0.878183	+	0.478324i	$0.158756\pi$
$644$		0			0
$645$	1.24072	+	1.24072i	0.0488533	+	0.0488533i
$646$		0			0
$647$		−	18.6188i		−	0.731979i	−0.930619	−	0.365989i	$-0.880731\pi$
$647$		−	18.6188i		−	0.731979i	0.930619	−	0.365989i	$-0.119269\pi$
$648$		0			0
$649$		−	31.3495i		−	1.23058i
$650$		0			0
$651$	−0.756707	−	0.756707i	−0.0296577	−	0.0296577i
$652$		0			0
$653$	−30.5099	+	30.5099i	−1.19395	+	1.19395i	−0.217995	+	0.975950i	$0.569952\pi$
$653$	−30.5099	+	30.5099i	−1.19395	+	1.19395i	−0.975950	+	0.217995i	$0.930048\pi$
$654$		0			0
$655$	−4.68874			−0.183204
$656$		0			0
$657$	34.8069			1.35795
$658$		0			0
$659$	21.1337	−	21.1337i	0.823252	−	0.823252i	−0.163321	−	0.986573i	$-0.552221\pi$
$659$	21.1337	−	21.1337i	0.823252	−	0.823252i	0.986573	+	0.163321i	$0.0522206\pi$
$660$		0			0
$661$	19.3455	+	19.3455i	0.752452	+	0.752452i	0.974936	−	0.222485i	$-0.0714167\pi$
$661$	19.3455	+	19.3455i	0.752452	+	0.752452i	−0.222485	+	0.974936i	$0.571417\pi$
$662$		0			0
$663$			3.13146i			0.121616i
$664$		0			0
$665$			2.05459i			0.0796734i
$666$		0			0
$667$	23.1032	+	23.1032i	0.894558	+	0.894558i
$668$		0			0
$669$	11.2220	−	11.2220i	0.433867	−	0.433867i
$670$		0			0
$671$	19.3582			0.747317
$672$		0			0
$673$	13.9541			0.537892			0.268946	−	0.963155i	$-0.413325\pi$
$673$	13.9541			0.537892			0.268946	+	0.963155i	$0.413325\pi$
$674$		0			0
$675$	−3.07541	+	3.07541i	−0.118373	+	0.118373i
$676$		0			0
$677$	−15.0295	−	15.0295i	−0.577629	−	0.577629i	0.356620	−	0.934249i	$-0.383929\pi$
$677$	−15.0295	−	15.0295i	−0.577629	−	0.577629i	−0.934249	+	0.356620i	$0.883929\pi$
$678$		0			0
$679$			13.1190i			0.503461i
$680$		0			0
$681$			13.0706i			0.500867i
$682$		0			0
$683$	−3.12623	−	3.12623i	−0.119622	−	0.119622i	0.644762	−	0.764384i	$-0.276957\pi$
$683$	−3.12623	−	3.12623i	−0.119622	−	0.119622i	−0.764384	+	0.644762i	$0.776957\pi$
$684$		0			0
$685$	−3.33358	+	3.33358i	−0.127370	+	0.127370i
$686$		0			0
$687$	−9.10693			−0.347451
$688$		0			0
$689$	15.6484			0.596158
$690$		0			0
$691$	5.25205	−	5.25205i	0.199797	−	0.199797i	−0.600116	−	0.799913i	$-0.704879\pi$
$691$	5.25205	−	5.25205i	0.199797	−	0.199797i	0.799913	+	0.600116i	$0.204879\pi$
$692$		0			0
$693$	−6.84742	−	6.84742i	−0.260112	−	0.260112i
$694$		0			0
$695$		−	19.6666i		−	0.745996i
$696$		0			0
$697$			12.1035i			0.458452i
$698$		0			0
$699$	7.97332	+	7.97332i	0.301579	+	0.301579i
$700$		0			0
$701$	15.3965	−	15.3965i	0.581517	−	0.581517i	−0.353803	−	0.935320i	$-0.615112\pi$
$701$	15.3965	−	15.3965i	0.581517	−	0.581517i	0.935320	+	0.353803i	$0.115112\pi$
$702$		0			0
$703$	−19.3025			−0.728007
$704$		0			0
$705$	5.82229			0.219280
$706$		0			0
$707$	0.844747	−	0.844747i	0.0317700	−	0.0317700i
$708$		0			0
$709$	−26.1685	−	26.1685i	−0.982778	−	0.982778i	0.0170765	−	0.999854i	$-0.494564\pi$
$709$	−26.1685	−	26.1685i	−0.982778	−	0.982778i	−0.999854	+	0.0170765i	$0.994564\pi$
$710$		0			0
$711$			24.2390i			0.909032i
$712$		0			0
$713$			10.5923i			0.396687i
$714$		0			0
$715$	7.84020	+	7.84020i	0.293207	+	0.293207i
$716$		0			0
$717$	−3.37645	+	3.37645i	−0.126096	+	0.126096i
$718$		0			0
$719$	18.8014			0.701173			0.350586	−	0.936530i	$-0.385982\pi$
$719$	18.8014			0.701173			0.350586	+	0.936530i	$0.385982\pi$
$720$		0			0
$721$	15.3945			0.573321
$722$		0			0
$723$	1.14372	−	1.14372i	0.0425352	−	0.0425352i
$724$		0			0
$725$	2.86338	+	2.86338i	0.106343	+	0.106343i
$726$		0			0
$727$		−	53.4505i		−	1.98237i	−0.132489	−	0.991185i	$-0.542297\pi$
$727$		−	53.4505i		−	1.98237i	0.132489	−	0.991185i	$-0.457703\pi$
$728$		0			0
$729$			2.55244i			0.0945348i
$730$		0			0
$731$	2.18652	+	2.18652i	0.0808713	+	0.0808713i
$732$		0			0
$733$	24.6798	−	24.6798i	0.911570	−	0.911570i	−0.0848259	−	0.996396i	$-0.527033\pi$
$733$	24.6798	−	24.6798i	0.911570	−	0.911570i	0.996396	+	0.0848259i	$0.0270334\pi$
$734$		0			0
$735$	−0.815159			−0.0300676
$736$		0			0
$737$	34.8555			1.28392
$738$		0			0
$739$	−11.8553	+	11.8553i	−0.436105	+	0.436105i	−0.890699	−	0.454594i	$-0.849784\pi$
$739$	−11.8553	+	11.8553i	−0.436105	+	0.436105i	0.454594	+	0.890699i	$0.349784\pi$
$740$		0			0
$741$	−3.16690	−	3.16690i	−0.116339	−	0.116339i
$742$		0			0
$743$		−	50.6920i		−	1.85971i	−0.367925	−	0.929855i	$-0.619932\pi$
$743$		−	50.6920i		−	1.85971i	0.367925	−	0.929855i	$-0.380068\pi$
$744$		0			0
$745$			2.73798i			0.100312i
$746$		0			0
$747$	2.09958	+	2.09958i	0.0768194	+	0.0768194i
$748$		0			0
$749$	−9.46571	+	9.46571i	−0.345870	+	0.345870i
$750$		0			0
$751$	4.54553			0.165869			0.0829343	−	0.996555i	$-0.473571\pi$
$751$	4.54553			0.165869			0.0829343	+	0.996555i	$0.473571\pi$
$752$		0			0
$753$	−17.7576			−0.647124
$754$		0			0
$755$	−14.1102	+	14.1102i	−0.513524	+	0.513524i
$756$		0			0
$757$	11.0294	+	11.0294i	0.400869	+	0.400869i	0.878539	−	0.477670i	$-0.158519\pi$
$757$	11.0294	+	11.0294i	0.400869	+	0.400869i	−0.477670	+	0.878539i	$0.658519\pi$
$758$		0			0
$759$		−	27.2705i		−	0.989856i
$760$		0			0
$761$			28.7744i			1.04307i	0.853229	+	0.521536i	$0.174641\pi$
$761$			28.7744i			1.04307i	−0.853229	+	0.521536i	$0.825359\pi$
$762$		0			0
$763$	−7.59547	−	7.59547i	−0.274974	−	0.274974i
$764$		0			0
$765$	−2.37241	+	2.37241i	−0.0857745	+	0.0857745i
$766$		0			0
$767$	−20.2188			−0.730058
$768$		0			0
$769$	29.5774			1.06659			0.533294	−	0.845930i	$-0.320954\pi$
$769$	29.5774			1.06659			0.533294	+	0.845930i	$0.320954\pi$
$770$		0			0
$771$	13.2616	−	13.2616i	0.477605	−	0.477605i
$772$		0			0
$773$	18.4444	+	18.4444i	0.663398	+	0.663398i	0.956180	−	0.292781i	$-0.0945807\pi$
$773$	18.4444	+	18.4444i	0.663398	+	0.663398i	−0.292781	+	0.956180i	$0.594581\pi$
$774$		0			0
$775$			1.31281i			0.0471574i
$776$		0			0
$777$		−	7.65828i		−	0.274739i
$778$		0			0
$779$	−12.2405	−	12.2405i	−0.438560	−	0.438560i
$780$		0			0
$781$	13.8562	−	13.8562i	0.495813	−	0.495813i
$782$		0			0
$783$	17.6122			0.629408
$784$		0			0
$785$	18.1395			0.647426
$786$		0			0
$787$	13.4883	−	13.4883i	0.480806	−	0.480806i	−0.424583	−	0.905389i	$-0.639579\pi$
$787$	13.4883	−	13.4883i	0.480806	−	0.480806i	0.905389	+	0.424583i	$0.139579\pi$
$788$		0			0
$789$	−4.39593	−	4.39593i	−0.156499	−	0.156499i
$790$		0			0
$791$			8.31678i			0.295711i
$792$		0			0
$793$		−	12.4851i		−	0.443357i
$794$		0			0
$795$	−3.37299	−	3.37299i	−0.119628	−	0.119628i
$796$		0			0
$797$	−28.1865	+	28.1865i	−0.998417	+	0.998417i	−0.999999	−	0.00158140i	$-0.999497\pi$
$797$	−28.1865	+	28.1865i	−0.998417	+	0.998417i	0.00158140	+	0.999999i	$0.499497\pi$
$798$		0			0
$799$	10.2606			0.362994
$800$		0			0
$801$	−26.9063			−0.950688
$802$		0			0
$803$	−43.6945	+	43.6945i	−1.54195	+	1.54195i
$804$		0			0
$805$	5.70528	+	5.70528i	0.201085	+	0.201085i
$806$		0			0
$807$		−	15.0081i		−	0.528312i
$808$		0			0
$809$			8.11833i			0.285425i	0.989764	+	0.142713i	$0.0455825\pi$
$809$			8.11833i			0.285425i	−0.989764	+	0.142713i	$0.954418\pi$
$810$		0			0
$811$	33.0046	+	33.0046i	1.15895	+	1.15895i	0.984702	+	0.174247i	$0.0557491\pi$
$811$	33.0046	+	33.0046i	1.15895	+	1.15895i	0.174247	+	0.984702i	$0.444251\pi$
$812$		0			0
$813$	7.05495	−	7.05495i	0.247428	−	0.247428i
$814$		0			0
$815$	18.4811			0.647363
$816$		0			0
$817$	−4.42253			−0.154725
$818$		0			0
$819$	−4.41622	+	4.41622i	−0.154315	+	0.154315i
$820$		0			0
$821$	22.7948	+	22.7948i	0.795543	+	0.795543i	0.982389	−	0.186846i	$-0.0598265\pi$
$821$	22.7948	+	22.7948i	0.795543	+	0.795543i	−0.186846	+	0.982389i	$0.559827\pi$
$822$		0			0
$823$		−	23.0983i		−	0.805155i	−0.915386	−	0.402577i	$-0.868114\pi$
$823$		−	23.0983i		−	0.805155i	0.915386	−	0.402577i	$-0.131886\pi$
$824$		0			0
$825$		−	3.37988i		−	0.117672i
$826$		0			0
$827$	34.0200	+	34.0200i	1.18299	+	1.18299i	0.978965	+	0.204027i	$0.0654032\pi$
$827$	34.0200	+	34.0200i	1.18299	+	1.18299i	0.204027	+	0.978965i	$0.434597\pi$
$828$		0			0
$829$	35.5005	−	35.5005i	1.23298	−	1.23298i	0.270173	−	0.962812i	$-0.412919\pi$
$829$	35.5005	−	35.5005i	1.23298	−	1.23298i	0.962812	−	0.270173i	$-0.0870809\pi$
$830$		0			0
$831$	−20.0498			−0.695519
$832$		0			0
$833$	−1.43655			−0.0497736
$834$		0			0
$835$	4.75578	−	4.75578i	0.164580	−	0.164580i
$836$		0			0
$837$	4.03742	+	4.03742i	0.139554	+	0.139554i
$838$		0			0
$839$			36.1815i			1.24912i	0.780976	+	0.624562i	$0.214722\pi$
$839$			36.1815i			1.24912i	−0.780976	+	0.624562i	$0.785278\pi$
$840$		0			0
$841$			12.6021i			0.434554i
$842$		0			0
$843$	13.6871	+	13.6871i	0.471409	+	0.471409i
$844$		0			0
$845$	−4.13587	+	4.13587i	−0.142278	+	0.142278i
$846$		0			0
$847$	6.19167			0.212748
$848$		0			0
$849$	2.15750			0.0740453
$850$		0			0
$851$	−53.6001	+	53.6001i	−1.83739	+	1.83739i
$852$		0			0
$853$	36.9036	+	36.9036i	1.26355	+	1.26355i	0.949358	+	0.314197i	$0.101735\pi$
$853$	36.9036	+	36.9036i	1.26355	+	1.26355i	0.314197	+	0.949358i	$0.398265\pi$
$854$		0			0
$855$		−	4.79852i		−	0.164106i
$856$		0			0
$857$		−	27.8872i		−	0.952608i	−0.879281	−	0.476304i	$-0.841976\pi$
$857$		−	27.8872i		−	0.952608i	0.879281	−	0.476304i	$-0.158024\pi$
$858$		0			0
$859$	−20.6313	−	20.6313i	−0.703931	−	0.703931i	0.261321	−	0.965252i	$-0.415842\pi$
$859$	−20.6313	−	20.6313i	−0.703931	−	0.703931i	−0.965252	+	0.261321i	$0.915842\pi$
$860$		0			0
$861$	4.85642	−	4.85642i	0.165506	−	0.165506i
$862$		0			0
$863$	−27.8828			−0.949141			−0.474570	−	0.880218i	$-0.657397\pi$
$863$	−27.8828			−0.949141			−0.474570	+	0.880218i	$0.657397\pi$
$864$		0			0
$865$	2.43254			0.0827088
$866$		0			0
$867$	−8.60936	+	8.60936i	−0.292389	+	0.292389i
$868$		0			0
$869$	−30.4281	−	30.4281i	−1.03220	−	1.03220i
$870$		0			0
$871$		−	22.4800i		−	0.761704i
$872$		0			0
$873$		−	30.6396i		−	1.03699i
$874$		0			0
$875$	0.707107	+	0.707107i	0.0239046	+	0.0239046i
$876$		0			0
$877$	4.71301	−	4.71301i	0.159147	−	0.159147i	−0.623042	−	0.782189i	$-0.714103\pi$
$877$	4.71301	−	4.71301i	0.159147	−	0.159147i	0.782189	+	0.623042i	$0.214103\pi$
$878$		0			0
$879$	−21.3962			−0.721677
$880$		0			0
$881$	46.3283			1.56084			0.780419	−	0.625256i	$-0.215006\pi$
$881$	46.3283			1.56084			0.780419	+	0.625256i	$0.215006\pi$
$882$		0			0
$883$	−1.42256	+	1.42256i	−0.0478728	+	0.0478728i	−0.730638	−	0.682765i	$-0.760777\pi$
$883$	−1.42256	+	1.42256i	−0.0478728	+	0.0478728i	0.682765	+	0.730638i	$0.260777\pi$
$884$		0			0
$885$	4.35812	+	4.35812i	0.146497	+	0.146497i
$886$		0			0
$887$			8.23550i			0.276521i	0.990396	+	0.138261i	$0.0441511\pi$
$887$			8.23550i			0.276521i	−0.990396	+	0.138261i	$0.955849\pi$
$888$		0			0
$889$		−	9.91643i		−	0.332587i
$890$		0			0
$891$	10.1477	+	10.1477i	0.339962	+	0.339962i
$892$		0			0
$893$	−10.3767	+	10.3767i	−0.347244	+	0.347244i
$894$		0			0
$895$	8.16476			0.272918
$896$		0			0
$897$	−17.5880			−0.587247
$898$		0			0
$899$	3.75907	−	3.75907i	0.125372	−	0.125372i
$900$		0			0
$901$	−5.94420	−	5.94420i	−0.198030	−	0.198030i
$902$		0			0
$903$		−	1.75464i		−	0.0583909i
$904$		0			0
$905$			23.0778i			0.767133i
$906$		0			0
$907$	−5.51759	−	5.51759i	−0.183209	−	0.183209i	0.609544	−	0.792752i	$-0.291353\pi$
$907$	−5.51759	−	5.51759i	−0.183209	−	0.183209i	−0.792752	+	0.609544i	$0.791353\pi$
$908$		0			0
$909$	−1.97292	+	1.97292i	−0.0654376	+	0.0654376i
$910$		0			0
$911$	−8.65180			−0.286647			−0.143323	−	0.989676i	$-0.545779\pi$
$911$	−8.65180			−0.286647			−0.143323	+	0.989676i	$0.545779\pi$
$912$		0			0
$913$	−5.27136			−0.174456
$914$		0			0
$915$	−2.69113	+	2.69113i	−0.0889659	+	0.0889659i
$916$		0			0
$917$	3.31544	+	3.31544i	0.109485	+	0.109485i
$918$		0			0
$919$			37.6570i			1.24219i	0.783735	+	0.621095i	$0.213312\pi$
$919$			37.6570i			1.24219i	−0.783735	+	0.621095i	$0.786688\pi$
$920$		0			0
$921$		−	18.8819i		−	0.622178i
$922$		0			0
$923$	−8.93651	−	8.93651i	−0.294149	−	0.294149i
$924$		0			0
$925$	−6.64315	+	6.64315i	−0.218426	+	0.218426i
$926$		0			0
$927$	−35.9541			−1.18089
$928$		0			0
$929$	41.6931			1.36791			0.683953	−	0.729526i	$-0.260259\pi$
$929$	41.6931			1.36791			0.683953	+	0.729526i	$0.260259\pi$
$930$		0			0
$931$	1.45281	−	1.45281i	0.0476140	−	0.0476140i
$932$		0			0
$933$	3.67771	+	3.67771i	0.120403	+	0.120403i
$934$		0			0
$935$		−	5.95635i		−	0.194793i
$936$		0			0
$937$		−	39.2632i		−	1.28267i	−0.767260	−	0.641336i	$-0.778381\pi$
$937$		−	39.2632i		−	1.28267i	0.767260	−	0.641336i	$-0.221619\pi$
$938$		0			0
$939$	−9.12318	−	9.12318i	−0.297724	−	0.297724i
$940$		0			0
$941$	−30.6071	+	30.6071i	−0.997762	+	0.997762i	−0.999998	−	0.00223595i	$-0.999288\pi$
$941$	−30.6071	+	30.6071i	−0.997762	+	0.997762i	0.00223595	+	0.999998i	$0.499288\pi$
$942$		0			0
$943$	−67.9799			−2.21373
$944$		0			0
$945$	4.34929			0.141483
$946$		0			0
$947$	−31.8816	+	31.8816i	−1.03601	+	1.03601i	−0.0366857	+	0.999327i	$0.511680\pi$
$947$	−31.8816	+	31.8816i	−1.03601	+	1.03601i	−0.999327	+	0.0366857i	$0.988320\pi$
$948$		0			0
$949$	28.1807	+	28.1807i	0.914783	+	0.914783i
$950$		0			0
$951$			12.2682i			0.397822i
$952$		0			0
$953$			32.5418i			1.05413i	0.849824	+	0.527066i	$0.176708\pi$
$953$			32.5418i			1.05413i	−0.849824	+	0.527066i	$0.823292\pi$
$954$		0			0
$955$	−6.44415	−	6.44415i	−0.208528	−	0.208528i
$956$		0			0
$957$	−9.67789	+	9.67789i	−0.312842	+	0.312842i
$958$		0			0
$959$	4.71440			0.152236
$960$		0			0
$961$	−29.2765			−0.944405
$962$		0			0
$963$	22.1073	−	22.1073i	0.712399	−	0.712399i
$964$		0			0
$965$	−2.94522	−	2.94522i	−0.0948101	−	0.0948101i
$966$		0			0
$967$		−	47.9565i		−	1.54218i	−0.636727	−	0.771089i	$-0.719712\pi$
$967$		−	47.9565i		−	1.54218i	0.636727	−	0.771089i	$-0.280288\pi$
$968$		0			0
$969$			2.40595i			0.0772904i
$970$		0			0
$971$	−16.5904	−	16.5904i	−0.532413	−	0.532413i	0.388877	−	0.921290i	$-0.372863\pi$
$971$	−16.5904	−	16.5904i	−0.532413	−	0.532413i	−0.921290	+	0.388877i	$0.872863\pi$
$972$		0			0
$973$	−13.9064	+	13.9064i	−0.445818	+	0.445818i
$974$		0			0
$975$	−2.17984			−0.0698109
$976$		0			0
$977$	23.3811			0.748028			0.374014	−	0.927423i	$-0.377981\pi$
$977$	23.3811			0.748028			0.374014	+	0.927423i	$0.377981\pi$
$978$		0			0
$979$	33.7765	−	33.7765i	1.07950	−	1.07950i
$980$		0			0
$981$	17.7393	+	17.7393i	0.566374	+	0.566374i
$982$		0			0
$983$			7.77765i			0.248068i	0.992278	+	0.124034i	$0.0395833\pi$
$983$			7.77765i			0.248068i	−0.992278	+	0.124034i	$0.960417\pi$
$984$		0			0
$985$		−	1.56639i		−	0.0499094i
$986$		0			0
$987$	−4.11698	−	4.11698i	−0.131045	−	0.131045i
$988$		0			0
$989$	−12.2807	+	12.2807i	−0.390504	+	0.390504i
$990$		0			0
$991$	22.8347			0.725370			0.362685	−	0.931912i	$-0.381860\pi$
$991$	22.8347			0.725370			0.362685	+	0.931912i	$0.381860\pi$
$992$		0			0
$993$	−6.41674			−0.203629
$994$		0			0
$995$	−4.85793	+	4.85793i	−0.154007	+	0.154007i
$996$		0			0
$997$	−8.83919	−	8.83919i	−0.279940	−	0.279940i	0.553145	−	0.833085i	$-0.313428\pi$
$997$	−8.83919	−	8.83919i	−0.279940	−	0.279940i	−0.833085	+	0.553145i	$0.813428\pi$
$998$		0			0
$999$			40.8609i			1.29278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.bd.a.561.13		44
4.3	odd	2		560.2.bd.a.421.20	yes	44
16.3	odd	4		560.2.bd.a.141.20	✓	44
16.13	even	4	inner	2240.2.bd.a.1681.13		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.20	✓	44	16.3	odd	4
560.2.bd.a.421.20	yes	44	4.3	odd	2
2240.2.bd.a.561.13		44	1.1	even	1	trivial
2240.2.bd.a.1681.13		44	16.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2240.bd (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.576404 - 0.576404i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} +2.33552i q^{9} +O(q^{10})\)	\(q+(0.576404 - 0.576404i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} +2.33552i q^{9} +(-2.93187 - 2.93187i) q^{11} +(-1.89090 + 1.89090i) q^{13} +0.815159 q^{15} +1.43655 q^{17} +(-1.45281 + 1.45281i) q^{19} +(-0.576404 - 0.576404i) q^{21} +8.06848i q^{23} +1.00000i q^{25} +(3.07541 + 3.07541i) q^{27} +(2.86338 - 2.86338i) q^{29} +1.31281 q^{31} -3.37988 q^{33} +(0.707107 - 0.707107i) q^{35} +(6.64315 + 6.64315i) q^{37} +2.17984i q^{39} +8.42537i q^{41} +(1.52206 + 1.52206i) q^{43} +(-1.65146 + 1.65146i) q^{45} +7.14252 q^{47} -1.00000 q^{49} +(0.828034 - 0.828034i) q^{51} +(-4.13783 - 4.13783i) q^{53} -4.14628i q^{55} +1.67481i q^{57} +(5.34634 + 5.34634i) q^{59} +(-3.30135 + 3.30135i) q^{61} +2.33552 q^{63} -2.67413 q^{65} +(-5.94425 + 5.94425i) q^{67} +(4.65071 + 4.65071i) q^{69} +4.72606i q^{71} -14.9033i q^{73} +(0.576404 + 0.576404i) q^{75} +(-2.93187 + 2.93187i) q^{77} +10.3784 q^{79} -3.46118 q^{81} +(0.898977 - 0.898977i) q^{83} +(1.01580 + 1.01580i) q^{85} -3.30093i q^{87} +11.5205i q^{89} +(1.89090 + 1.89090i) q^{91} +(0.756707 - 0.756707i) q^{93} -2.05459 q^{95} -13.1190 q^{97} +(6.84742 - 6.84742i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q+O(q^{10}) \) 44 * q	\( 44 q - 12 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 12 q^{29} + 28 q^{37} + 44 q^{43} - 44 q^{49} + 8 q^{51} - 12 q^{53} - 24 q^{59} - 16 q^{61} - 28 q^{63} - 40 q^{65} + 28 q^{67} + 40 q^{69} - 12 q^{77} + 16 q^{79} + 20 q^{81} + 16 q^{85} + 88 q^{93} + 32 q^{95} - 28 q^{99}+O(q^{100}) \) 44 * q - 12 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 12 * q^29 + 28 * q^37 + 44 * q^43 - 44 * q^49 + 8 * q^51 - 12 * q^53 - 24 * q^59 - 16 * q^61 - 28 * q^63 - 40 * q^65 + 28 * q^67 + 40 * q^69 - 12 * q^77 + 16 * q^79 + 20 * q^81 + 16 * q^85 + 88 * q^93 + 32 * q^95 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more